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An estimation for the ascending numbers of knots by $Γ$ -polynomials

Ryuji Higa

Department of Mathematics, Graduate School of Science, Kobe University, Rokko, Nada-ku, Kobe 657-8501, Japan

https://doi.org/10.1142/S0218216519500962Cited by:1 (Source: Crossref)

Abstract

For a knot, the ascending number is the minimum number of crossing changes which are needed to obtain an descending diagram. We study the $Γ$ -polynomial of knots with a given ascending number. We give a lower bound of the ascending numbers by using $Γ$ -polynomials. We estimate the ascending numbers for 65 prime knots up to 10 crossings by using $Γ$ -polynomials, Conway polynomials, and the determinants.

Keywords:

AMSC: 57M25

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